A seismic equation of state II. Shear properties and thermodynamics of the lower mantle

Abstract

For most solids at normal conditions the effect of temperature on the elastic properties is controlled mainly by the variation of volume. Volume dependent extrinsic effects dominate at low pressure and high temperature. Under these conditions one expects that the relative changes in shear velocity, due to lateral temperature gradients in the mantle, should be similar to changes in compressional velocity. However, at high pressure, the extrinsic contribution is suppressed, particularly for the bulk modulus, and variations of seismic velocities are due primarily to changes in the rigidity. Seismic data for the lower mantle are used to estimate the two Grüneisen parameters and related parameters such as the temperature and pressure derivatives of the elastic moduli and thermal expansion. Standard assumptions about the volume dependence of the elastic moduli based on high temperature behavior of solids are shown to be inaccurate for the lower mantle. The Grüneisen-type parameters for the lower mantle are (∂ ln K S ∂ ln ρ) P = δ S = 1.8 − 1.0, (∂ ln K S ∂ ln ρ) S = 3 − 3.8, (∂ ln G ∂ ln ρ) P = 5.8 − 7.0, (∂ ln G ∂ ln ρ) S = 2.4 − 2.6 and γ = 1.3 − 1.1 . These are based on the radial and lateral variations of seismic velocity and density. The zero-pressure high-temperature values for the coefficient of thermal expansion and the Grüneisen ratio are estimated as α 0 = 3.8 × 10 −5 K −1 and γ 0 = 1.4. The seismic data imply (∂ ln γ ∂ ln ρ) = −1 + ϵ and −(∂ ln α ∂ ln ρ) ∼ 2 − 3 . The effect of temperature on the pressure derivatives of the moduli is also estimated. The lattice conductivity, K L, increases rapidly with depth, contributing to a lowering of the Rayleigh number in the lower mantle and a large thickness for deep thermal boundary layers. Temperature is less effective in altering density and seismic velocity at depth than assumed in geophysical modeling. Temperature induced phase changes are more important than temperature per se. These considerations cast doubt on the thermal interpretation of deep slab anomalies and, therefore, on the deep slab penetration hypothesis.